Christopher Tanev, Loui Eriksson, Josh Leivo and Markus Granlund scored, Troy Stecher had two assists, and Jacob Markstrom made 31 saves for the Canucks (15-16-4), who are 4-0-1 in their past five games after going 1-10-2 in the previous 13.
All four lines scored for Vancouver, which took a 3-0 lead in the opening 11:12.
[WATCH: All Flyers vs. Canucks highlights]
"Our top two lines have been getting a lot of people talking about our young players," coach Travis Green said. "But it was nice tonight that our third and fourth lines, I thought they played a good game tonight and calmed the waters when it was going back and forth a bit."
Scott Laughton scored for the Flyers (12-15-4), who lost the final four of their five-game road trip. Philadelphia is 3-8-3 in its past 14 games and has allowed at least four goals in seven of the past nine.
"It's one of the most frustrating times in my professional career, 100 percent," defenseman Radko Gudas said. "We let our goalies down, we let our fans down, we let everybody down, so it's not on the coach's shoulders. We have to perform better, we have to play as a group better."
Video: PHI@VAN: Tanev backhands puck past Stolarz
Flyers goalie Anthony Stolarz started after playing Friday in a 4-1 loss to the Edmonton Oilers, but he allowed two goals on four shots before leaving with a lower-body injury at 8:14 of the first period.
Alex Lyon made 17 saves in relief while emergency backup goalie Rylan Toth, who plays at the University of British Columbia, waited outside the locker room. Toth, who played three seasons in the Western Hockey League, did not come to the bench and would have signed a contract only if Lyon was injured.
Philadelphia coach Dave Hakstol did not have an update on Stolarz after the game.
Hakstol bristled at questions about the Flyers hanging their heads after falling behind in the first period for the fifth game in a row.
"Didn't happen tonight. Unless you watched a different game than I watched," he said. "Our guys pushed like [heck] all the way through that game, so that didn't happen."
Tanev scored on a delayed penalty to make it 1-0 at 4:13, skating into the slot unchecked before lifting a backhand under the Stolarz's blocker arm for his first goal of the season.
"No one was really around," Tanev said. "The seas almost parted."
Eriksson scored on a wrist shot from the slot to make it 2-0 at 8:09.
"The first two were probably the first two scoring chances against," Hakstol said. "It's tough when you are battling from behind, but we did battle."
Leivo scored with a sharp-angled shot that bounced past Lyon off defenseman Andrew MacDonald's skate to make it 3-0 at 11:12.
Laughton scored on a solo rush at 16:29 of the first to make it 3-1.
"It's a pretty empty feeling right now," Laughton said. "We've got a tight group off the ice, but it's got to translate on the ice and it's got to happen quick here."
Boeser made it 4-1 at 12:07 of the second period on a screened shot from the blue line off a give-and-go with Troy Stecher after a won face-off by Elias Pettersson, who extended his point streak to six games (three goals, nine assists).
"Honestly, I was just trying to get a puck on net there and get a rebound," said Boeser, who has seven goals and two assists in his past eight games. "It was pretty lucky."
Granlund scored into an empty net with 4:31 remaining for the 5-1 final score.
Video: PHI@VAN: Eriksson whips puck home to double lead
They said it
"A night like tonight, you are angry when you come off the ice and walk out of the rink, so we get a long trip home tomorrow, we got to get things cleared up in our minds. There is a ton of things in this hockey game that we did right, and if you want to take a look at it and break it down, we had to chase the game again from early on and that's a really hard thing to do, but in terms of the overall effort and some of the opportunities we were able to generate, there's a ton of good things there." -- Flyers coach Dave Hakstol
"I don't think it was our best hockey, but we found a way to get it done, and I think that's encouraging." -- Canucks forward Brock Boeser
Need to know
Lyon was recalled from Lehigh Valley of the American Hockey League on Thursday after goalie Michal Neuvirth returned to Philadelphia for the expected birth of his child. … Flyers forward Jakub Voracek had his point streak end at seven games (three goals, five assists) and remains two points shy of 600 in the NHL. … Markstrom has a .942 save percentage during a personal four-game winning streak.
Flyers: Host the Detroit Red Wings on Tuesday (7 p.m. ET; TVAS, NBCSP, FS-D, NHL.TV)
Canucks: Host the Edmonton Oilers on Sunday (10 p.m. ET; SNP, SNW, NHL.TV)
Video: Boeser, Markstrom propel Canucks past Flyers